The Cosine rule

Back to : Algebra | Sequence and Series

To solve a triangle is to find the lengths of each of its sides and all its angles.
The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known.
The cosine rule is used when we are given either

          [a] three sides or

          [b] two sides and the included angle.
By changing which sides of the triangle play the roles of ab, and c in the original formula, the following two formulas also state the law of cosines:

Skill builder questions

Practice worksheet – 1 Cosine rule worksheet – 1
Practice worksheet – 2 Cosine rule worksheet – 2
Practice worksheet – 3 Cosine rule worksheet – 3